Question

Two objects of same mass, namely $A$ and $B$ hit a man with a speed of $20km/hr$ and $50km/hr$ respectively and comes to rest instantaneously. Which object will exert more force on that man? Justify your answer.

Answer 1

Let the mass of each object be m

Speed of A = 20km/h

Speed of B = 50km/h

Momentum of A = mass $\times$ velocity

= m $\times$20

= 20m

Momentum of B = 50m

Now, when both balls come to rest after hitting man,

final momentum of A = 0

final momentum of B = 0

Now, according to Newton's second law, the rate of change of momentum is proportional to the force applied.

As both balls come to rest after hitting the man, in the same time (say 't')

Rate of change of momentum of A = $\frac{20m}{t}$

Rate of change of momentum of B = $\frac{50m}{t}$

As the rate of change of momentum of B is greater than A, B will exert more force on a man.